How does the Square Root Calculator work?

Factor the number into prime factors Then: Pair up identical prime factors Then: Take one factor from each pair and multiply them Then: Any unpaired factors stay inside the radical symbol.

Can you give an example of how to use the Square Root Calculator?

Example: Input √144 gives a result of 12 (12 × 12 = 144).

Is the Square Root Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Square Root Calculator?

Our Square Root Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Square Root Calculator

Number

The square root of a number x is a value r such that r² = x. Every positive number has two square roots: a positive (principal) root and a negative root. Only zero has a single square root: zero itself.

n	n²	√(n²)
1	1	1
2	4	2
3	9	3
4	16	4
5	25	5
6	36	6
7	49	7
8	64	8
9	81	9
10	100	10
11	121	11
12	144	12
13	169	13
14	196	14
15	225	15
16	256	16
17	289	17
18	324	18
19	361	19
20	400	20

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Pro Tip

To check your answer: square it. If r = √x, then r² should equal x exactly.

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Did You Know?

The ancient Babylonians calculated square roots using a method equivalent to Newton's method around 1700 BC — over 3,500 years ago.

References

›Square root — Wikipedia
›Square Roots — Khan Academy

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Square Root Calculator

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Square root of zero

Square root of a negative number

Perfect Squares — 1 through 20

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Square Root Calculator

n	n²	√(n²)
1	1	1
2	4	2
3	9	3
4	16	4
5	25	5
6	36	6
7	49	7
8	64	8
9	81	9
10	100	10
11	121	11
12	144	12
13	169	13
14	196	14
15	225	15
16	256	16
17	289	17
18	324	18
19	361	19
20	400	20

n	n²	√(n²)
1	1	1
2	4	2
3	9	3
4	16	4
5	25	5
6	36	6
7	49	7
8	64	8
9	81	9
10	100	10
11	121	11
12	144	12
13	169	13
14	196	14
15	225	15
16	256	16
17	289	17
18	324	18
19	361	19
20	400	20

n	n²	√(n²)
1	1	1
2	4	2
3	9	3
4	16	4
5	25	5
6	36	6
7	49	7
8	64	8
9	81	9
10	100	10
11	121	11
12	144	12
13	169	13
14	196	14
15	225	15
16	256	16
17	289	17
18	324	18
19	361	19
20	400	20